With suitable choice of these constants a, b, c, u, v, w, various transmission properties such as attenuation, phase shift and group delay may be established for a quadrupole of this type used for selective filtering, line matching, noise measurements, voice analysis etc. The numerator coefficients a, b, c may be of either sign (or possibly zero) whereas the denominator coefficients u, v, w are all positive except that w may be zero in a limiting case. A second-order filter conforming to the transfer function of equation (1) can be realized by means of three cascaded stages each including an operational amplifier as is well known per se, e.g. from U.S. Pat. No. 3,715,679 which discloses an all-pass delay equalizer of this type. More generally, an n.sup.th -order filter can be constructed from n such cascaded stages, using an integrating amplifier in each stage except the last one; see, for example, the handbook by U. Tietze and Ch. Schenk entitled HALBLEITER-SCHALTUNGSTECHNIK, Third Edition (1974), published by Springer-Verlag, pages 357 and 358.
Circuit arrangements are also known which permit a limited adjustment of such filters, e.g. a switchover between a Bessel and a Butterworth characteristic or a shifting of the limiting or central frequencies of their bands. A more fundamental transformation, e.g. a changeover from a band-pass to an all-pass characteristic, is not realizable with these conventional systems.